{"id":22844,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/stat-3115-homework-9"},"modified":"2017-08-03T16:11:44","modified_gmt":"2017-08-03T16:11:44","slug":"stat-3115-homework-9","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/stat-3115-homework-9\/","title":{"rendered":"STAT 3115 \u2013 Homework #9"},"content":{"rendered":"<div class=\"the_content_wrapper\">\n<p>Stat3115<br \/> STAT 3115 \u2013 Homework #9<br \/> Due Date: Thursday, April 20th, Beginning of Class<br \/> Note: Please include the following information on the first page of your completed homework.<br \/> 1. Your Name<br \/> 2. STAT 3115 \u2013 Section: 1C<br \/> 3. Homework #9<br \/> 4. Due Date: Thursday, April 20th<br \/> 5. List of students you worked with on this assignment (if applicable)<br \/> Guidelines: Please remember to show your work and explain your answers as necessary. Answers that<br \/> are not supported by reasoning will not receive full credit. Homework should be stapled if it is longer<br \/> than one page. Numbered problems are from Devore, 9th ed. unless otherwise noted.<br \/> Section 5.4:<br \/> 1- Ice cream manufacturing. Ice cream cartons from a certain manufacturer have a true average<br \/> weight of 12 ounces, with a population standard deviation of 1 ounce. You take a random sample<br \/> of 100 cartons.<br \/> a. Find the expected value and standard deviation of the average weight (?????) in the sample of 100<br \/> cartons.<br \/> b. Find the (approximate) probability that the average weight among these 100 cartons is between<br \/> 11.8 and 12.15 ounces.<br \/> c. What theorem are you using to calculate the probability in b? What assumption is necessary in<br \/> order for this theorem to hold?<br \/> 2- Young\u2019s modulus is a quantitative measure of stiffness of an elastic material. Suppose that for<br \/> aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and<br \/> 1.6 GPa, respectively.<br \/> a. If ????? is the sample mean Young\u2019s modulus for a random sample of ???? = 16 sheets, where is the<br \/> sampling distribution of ????? centered, and what is the standard deviation of the ????? distribution?<br \/> b. Answer the questions posed in part (a) for a sample size of ???? = 64 sheets.<br \/> c. For which of the two random samples, the one of part (a) or the one of part (b), is ????? more likely<br \/> to be within 1 GPa of 70 GPa? Explain your reasoning.<br \/> Now suppose the distribution is normal (the cited article makes that assumption and even<br \/> includes the corresponding normal density curve).<br \/> d. Calculate ????(69 = ????? = 71) when ???? = 16.<br \/> e. How likely is it that the sample mean diameter exceeds 71 when ???? = 25?<br \/> Page 1 of 2<br \/> Section 7.1:<br \/> 3- Helium porosity. Assume that the helium porosity (in percentage) of coal samples taken from a<br \/> particular seam is normally distributed with a population standard deviation of 0.69. We are<br \/> interested in constructing a confidence interval for the true average helium porosity (\u00b5) in the seam.<br \/> a. Find a 95% confidence interval for \u00b5 when a random sample of 25 coal samples are taken<br \/> yielding a sample mean of 4.56.<br \/> b. Find a 95% confidence interval for \u00b5 when a random sample of 100 coal samples are taken<br \/> yielding a sample mean of 4.56.<br \/> c. Compare the widths of a and b, stating how the sample size affects the width.<br \/> d. Find a 98% confidence interval for \u00b5 when a random sample of 100 coal samples are taken<br \/> yielding a sample mean of 4.56.<br \/> e. Compare the widths of b and d, stating how the confidence level affects the width.<br \/> f. How large of a sample size is needed to ensure a width of 0.4 for a 95% confidence<br \/> interval?<br \/> 4- Each of the following is a confidence interval for ???? = true average (i.e., population mean)<br \/> resonance frequency (Hz) for all tennis rackets of a certain type: (114.4, 115.6) (114.1, 115.9)<br \/> a. What is the value of the sample mean resonance frequency?<br \/> b. Both intervals were calculated from the same sample data. The confidence level for one of<br \/> these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence<br \/> level, and why?<br \/> Section 7.2:<br \/> 5- Night School Students. A sample of 60 night school students is obtained in order to estimate the<br \/> mean age of all night school students at a university. The result is a sample mean of 25.3 years and<br \/> a sample standard deviation of 4.<br \/> a. Give a point estimate for \u00b5, the population mean age of all night school students.<br \/> b. Find a 99% confidence interval for \u00b5.<br \/> 6- A sample of 56 research cotton samples resulted in a sample average percentage elongation of 8.17<br \/> and a sample standard deviation of 1.42 (\u201cAn Apparent Relation Between the Spiral Angle f, the<br \/> Percent Elongation E1, and the Dimensions of the Cotton Fiber,\u201d Textile Research J., 1978: 407\u2013<br \/> 410). Calculate a 95% large-sample CI for the true average percentage elongation m. What<br \/> assumptions are you making about the distribution of percentage elongation?<br \/> Page 2 of 2<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Stat3115 STAT 3115 \u2013 Homework #9 Due Date: Thursday, April 20th, Beginning of Class Note: Please include the following information on the first page of your completed homework. 1. Your Name 2. STAT 3115 \u2013 Section: 1C 3. Homework #9 <a href=\"https:\/\/www.benedictsol.com\/blogs\/stat-3115-homework-9\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-22844","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/22844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=22844"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/22844\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=22844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=22844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=22844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}